Related papers: Priority arguments and separation problems
One of the long-standing problems on logic programming is to express {\it priority}-related operations -- default reasoning, if-then-else, cut, exception handling, etc -- in a high-level way. We argue that this problem can be solved by…
Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision…
Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…
Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…
A series of works has established rewriting as an essential tool in order to prove coherence properties of algebraic structures, such as MacLane's coherence theorem for monoidal categories, based on the observation that, under reasonable…
Prioritized Default Logic presents an optimal solution for addressing real-world problems characterized by incomplete information and the need to establish preferences among diverse scenarios. Although it has reached great success in the…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Reward modelling from preference data is a crucial step in aligning large language models (LLMs) with human values, requiring robust generalisation to novel prompt-response pairs. In this work, we propose to frame this problem in a causal…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…
Explainable recommendation systems leverage transparent reasoning to foster user trust and improve decision-making processes. Current approaches typically decouple recommendation generation from explanation creation, violating causal…
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class. An enumeration problem belongs to Constant-Delaylin if for an input of size n it…
The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…